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6.2 Formation rate

An estimate of the rate of the collapse of SMSs can be derived from the quasar luminosity function. Haehnelt [99] has used the quasar luminosity function to compute the rate of GW bursts from supermassive black holes, assuming that each quasar emits one such burst during its lifetime (and that each quasar is a supermassive black hole). If it is assumed that each of these bursts is due to the formation of a supermassive black hole via the collapse of a SMS, then Haehnelt’s rate estimates can be used as estimates of the rate of SMS collapse. This rate is likely an overestimate of the SMS collapse rate because many SMBHs may have been formed via merger. Haehnelt predicts that the integrated event rate through redshift z = 4.5 ranges from ~ 10-6 yr-1 for M = 108 M o . objects to -1 ~ 1 yr for 6 M = 10 Mo . objects. Thus, as in the case of Population III stars, a reasonable occurrence rate can be determined for an observation (luminosity) distance of 50 Gpc.
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